A note on the projective representations of $p$-solvable and $π$-separable group

Abstract: Following Gluck and Wolf we complete the Itô--Michler's Theorem for the projective representations of a $p$-solvable or $π$-separable group, and then we relate the projective irreducible modules of such a group with those of its Sylow $p$-subroups and Hall $π$-subgroups.